Theorem 3ad2antl1 1126

Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 4-Aug-2007.)

Hypothesis

Ref	Expression
3ad2antl.1	|- ( ( ph /\ ch ) -> th )

Assertion

Ref	Expression
3ad2antl1	|- ( ( ( ph /\ ps /\ ta ) /\ ch ) -> th )

Proof of Theorem 3ad2antl1

Step	Hyp	Ref	Expression
1		3ad2antl.1	. . 3 |- ( ( ph /\ ch ) -> th )
2	1	adantlr 466	. 2 |- ( ( ( ph /\ ta ) /\ ch ) -> th )
3	2	3adantl2 1121	1 |- ( ( ( ph /\ ps /\ ta ) /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 945

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 947

This theorem is referenced by:  acexmid  5727  ordiso2  6872  addlocpr  7292  distrlem1prl  7338  distrlem1pru  7339  ltsopr  7352  addcanprlemu  7371  fzo1fzo0n0  9853  muldvds2  11367  dvds2add  11375  dvds2sub  11376  dvdstr  11378  cnpnei  12230  upxp  12283